I've read from different people on the forum here that doing a mite drop count should be over a 24 hour period or a 72 hour period. Is the 72 hour check more accurate?

I think 24 is the way to go because the levels used to gauge if you should or shouldn't treat are based off of a 24 hour count. I am not sure what the levels would be if you were to increase the time to 72 hours.

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What is the recommended way to do the other hive's drop count?

You can take about a cup of bees and put them in a mason jar with a cover of screen. Put powdered sugar in the jar and shake the bees to coat them. Pour out the powered sugar into a small container and count the mites. An easy way to get a cup of bees is to take a frame or two of bees and shake them into a plastic container (so they can't climb up the walls easily) then pour them into a 1 cup measuring cup. The remaining bees can go back into the hive.

Basically the powdered sugar is going to dislodge the mites from the bees.

Also, the sticky boards should come with a screen so that the bees don't get trapped on the board when they walk on it, but the mites still get stuck. I'm pretty sure this is included in case you don't have a SBB.